We present the first finite time global convergence analysis of policy gradient in the context of infinite horizon average reward Markov decision processes (MDPs). Specifically, we focus on ergodic tabular MDPs with finite state and action spaces. Our analysis shows that the policy gradient iterates converge to the optimal policy at a sublinear rate of $O\left({\frac{1}{T}}\right),$ which translates to $O\left({\log(T)}\right)$ regret, where $T$ represents the number of iterations. Prior work on performance bounds for discounted reward MDPs cannot be extended to average reward MDPs because the bounds grow proportional to the fifth power of the effective horizon. Thus, our primary contribution is in proving that the policy gradient algorithm converges for average-reward MDPs and in obtaining finite-time performance guarantees. In contrast to the existing discounted reward performance bounds, our performance bounds have an explicit dependence on constants that capture the complexity of the underlying MDP. Motivated by this observation, we reexamine and improve the existing performance bounds for discounted reward MDPs. We also present simulations to empirically evaluate the performance of average reward policy gradient algorithm.

With the long term accumulation of high quality educational data, artificial intelligence has shown excellent performance in knowledge tracing. However, due to the lack of interpretability and transparency of some algorithms, this approach will result in reduced stakeholder trust and a decreased acceptance of intelligent decisions. Therefore, algorithms need to achieve high accuracy, and users need to understand the internal operating mechanism and provide reliable explanations for decisions. This paper thoroughly analyzes the interpretability of KT algorithms. First, the concepts and common methods of explainable artificial intelligence and knowledge tracing are introduced. Next, explainable knowledge tracing models are classified into two categories: transparent models and black box models. Then, the interpretable methods used are reviewed from three stages: ante hoc interpretable methods, post hoc interpretable methods, and other dimensions. It is worth noting that current evaluation methods for explainable knowledge tracing are lacking. Hence, contrast and deletion experiments are conducted to explain the prediction results of the deep knowledge tracing model on the ASSISTment2009 by using three XAI methods. Moreover, this paper offers some insights into evaluation methods from the perspective of educational stakeholders. This paper provides a detailed and comprehensive review of the research on explainable knowledge tracing, aiming to offer some basis and inspiration for researchers interested in the interpretability of knowledge tracing.

Transfer learning has recently shown significant performance across various tasks involving deep neural networks. In these transfer learning scenarios, the prior distribution for downstream data becomes crucial in Bayesian model averaging (BMA). While previous works proposed the prior over the neural network parameters centered around the pre-trained solution, such strategies have limitations when dealing with distribution shifts between upstream and downstream data. This paper introduces nonparametric transfer learning (NPTL), a flexible posterior sampling method to address the distribution shift issue within the context of nonparametric learning. The nonparametric learning (NPL) method is a recent approach that employs a nonparametric prior for posterior sampling, efficiently accounting for model misspecification scenarios, which is suitable for transfer learning scenarios that may involve the distribution shift between upstream and downstream tasks. Through extensive empirical validations, we demonstrate that our approach surpasses other baselines in BMA performance. In Bayesian deep learning, we regard the parameters of a deep neural network as random variables. Instead of optimizing for a single-point estimate of these parameters, this approach involves inferring the posterior distribution of these parameters given the provided training data and predefined parameter prior distribution. After we have the posterior distribution, we make predictions through Bayesian model averaging (BMA). BMA entails computing predictions from multiple parameter values and weighting them based on their respective densities within the posterior. The success of Bayesian deep learning often depends on the choice of the prior distribution.

One aspect of the algorithmic lens in theoretical computer science is a view on other scientific disciplines that focuses on satisfactory solutions that adhere to real-world constraints, as opposed to solutions that would be optimal ignoring such constraints. The algorithmic lens has provided a unique and important perspective on many academic fields, including molecular biology, ecology, neuroscience, quantum physics, economics, and social science. This thesis applies the algorithmic lens to Bayesian epistemology. Traditional Bayesian epistemology provides a comprehensive framework for how an individual's beliefs should evolve upon receiving new information. However, these methods typically assume an exhaustive model of such information, including the correlation structure between different pieces of evidence. In reality, individuals might lack such an exhaustive model, while still needing to form beliefs. Beyond such informational constraints, an individual may be bounded by limited computation, or by limited communication with agents that have access to information, or by the strategic behavior of such agents. Even when these restrictions prevent the formation of a *perfectly* accurate belief, arriving at a *reasonably* accurate belief remains crucial. In this thesis, we establish fundamental possibility and impossibility results about belief formation under a variety of restrictions, and lay the groundwork for further exploration.

Decentralized and lifelong-adaptive multi-agent collaborative learning aims to enhance collaboration among multiple agents without a central server, with each agent solving varied tasks over time. To achieve efficient collaboration, agents should: i) autonomously identify beneficial collaborative relationships in a decentralized manner; and ii) adapt to dynamically changing task observations. In this paper, we propose DeLAMA, a decentralized multi-agent lifelong collaborative learning algorithm with dynamic collaboration graphs. To promote autonomous collaboration relationship learning, we propose a decentralized graph structure learning algorithm, eliminating the need for external priors. To facilitate adaptation to dynamic tasks, we design a memory unit to capture the agents' accumulated learning history and knowledge, while preserving finite storage consumption. To further augment the system's expressive capabilities and computational efficiency, we apply algorithm unrolling, leveraging the advantages of both mathematical optimization and neural networks. This allows the agents to `learn to collaborate' through the supervision of training tasks. Our theoretical analysis verifies that inter-agent collaboration is communication efficient under a small number of communication rounds. The experimental results verify its ability to facilitate the discovery of collaboration strategies and adaptation to dynamic learning scenarios, achieving a 98.80% reduction in MSE and a 188.87% improvement in classification accuracy. We expect our work can serve as a foundational technique to facilitate future works towards an intelligent, decentralized, and dynamic multi-agent system. Code is available at https://github.com/ShuoTang123/DeLAMA.

An important and unsolved problem in computer vision is to ensure that the algorithms are robust to changes in image domains. We address this problem in the scenario where we have access to images from the target domains but no annotations. Motivated by the challenges of the OOD-CV benchmark where we encounter real world Out-of-Domain (OOD) nuisances and occlusion, we introduce a novel Bayesian approach to OOD robustness for object classification. Our work extends Compositional Neural Networks (CompNets), which have been shown to be robust to occlusion but degrade badly when tested on OOD data. We exploit the fact that CompNets contain a generative head defined over feature vectors represented by von Mises-Fisher (vMF) kernels, which correspond roughly to object parts, and can be learned without supervision. We obverse that some vMF kernels are similar between different domains, while others are not. This enables us to learn a transitional dictionary of vMF kernels that are intermediate between the source and target domains and train the generative model on this dictionary using the annotations on the source domain, followed by iterative refinement. This approach, termed Unsupervised Generative Transition (UGT), performs very well in OOD scenarios even when occlusion is present. UGT is evaluated on different OOD benchmarks including the OOD-CV dataset, several popular datasets (e.g., ImageNet-C [9]), artificial image corruptions (including adding occluders), and synthetic-to-real domain transfer, and does well in all scenarios outperforming SOTA alternatives (e.g. up to 10% top-1 accuracy on Occluded OOD-CV dataset).

Graphs are ubiquitous in social networks and biochemistry, where Graph Neural Networks (GNN) are the state-of-the-art models for prediction. Graphs can be evolving and it is vital to formally model and understand how a trained GNN responds to graph evolution. We propose a smooth parameterization of the GNN predicted distributions using axiomatic attribution, where the distributions are on a low-dimensional manifold within a high-dimensional embedding space. We exploit the differential geometric viewpoint to model distributional evolution as smooth curves on the manifold. We reparameterize families of curves on the manifold and design a convex optimization problem to find a unique curve that concisely approximates the distributional evolution for human interpretation. Extensive experiments on node classification, link prediction, and graph classification tasks with evolving graphs demonstrate the better sparsity, faithfulness, and intuitiveness of the proposed method over the state-of-the-art methods. Graph neural networks (GNN) are now the state-of-the-art method for graph representation in many applications, such as social network modeling Kipf & Welling (2017) and molecule property prediction Wu et al. (2017), pose estimation in computer vision Yang et al. (2021), smart cities Ye et al. (2020), fraud detection Wang et al. (2019), and recommendation systems Ying et al. (2018). A GNN outputs a probability distribution Pr(Y |G; θ) of Y, the class random variable of a node (node classification), a link (link prediction), or a graph (graph classification), using trained parameters θ.

A recent research trend involves treating database index structures as Machine Learning (ML) models. In this domain, single or multiple ML models are trained to learn the mapping from keys to positions inside a data set. This class of indexes is known as "Learned Indexes." Learned indexes have demonstrated improved search performance and reduced space requirements for one-dimensional data. The concept of one-dimensional learned indexes has naturally been extended to multi-dimensional (e.g., spatial) data, leading to the development of "Learned Multi-dimensional Indexes". This survey focuses on learned multi-dimensional index structures. Specifically, it reviews the current state of this research area, explains the core concepts behind each proposed method, and classifies these methods based on several well-defined criteria. We present a taxonomy that classifies and categorizes each learned multi-dimensional index, and survey the existing literature on learned multi-dimensional indexes according to this taxonomy. Additionally, we present a timeline to illustrate the evolution of research on learned indexes. Finally, we highlight several open challenges and future research directions in this emerging and highly active field.

In this paper, we propose Posterior Sampling Reinforcement Learning for Zero-sum Stochastic Games (PSRL-ZSG), the first online learning algorithm that achieves Bayesian regret bound of $O(HS\sqrt{AT})$ in the infinite-horizon zero-sum stochastic games with average-reward criterion. Here $H$ is an upper bound on the span of the bias function, $S$ is the number of states, $A$ is the number of joint actions and $T$ is the horizon. We consider the online setting where the opponent can not be controlled and can take any arbitrary time-adaptive history-dependent strategy. Our regret bound improves on the best existing regret bound of $O(\sqrt[3]{DS^2AT^2})$ by Wei et al. (2017) under the same assumption and matches the theoretical lower bound in $T$.

Causal discovery in the presence of unobserved common causes from observational data only is a crucial but challenging problem. We categorize all possible causal relationships between two random variables into the following four categories and aim to identify one from observed data: two cases in which either of the direct causality exists, a case that variables are independent, and a case that variables are confounded by latent confounders. Although existing methods have been proposed to tackle this problem, they require unobserved variables to satisfy assumptions on the form of their equation models. In our previous study (Kobayashi et al., 2022), the first causal discovery method without such assumptions is proposed for discrete data and named CLOUD. Using Normalized Maximum Likelihood (NML) Code, CLOUD selects a model that yields the minimum codelength of the observed data from a set of model candidates. This paper extends CLOUD to apply for various data types across discrete, mixed, and continuous. We not only performed theoretical analysis to show the consistency of CLOUD in terms of the model selection, but also demonstrated that CLOUD is more effective than existing methods in inferring causal relationships by extensive experiments on both synthetic and real-world data.